Absolutely expedient algorithms for learning Nash equilibria

This paper considers a multi-person discrete game with random payoffs. The distribution of the random payoff is unknown to the players and further none of the players know the strategies or the actual moves of other players. A class of absolutely expedient learning algorithms for the game based on a decentralised team of Learning Automata is presented. These algorithms correspond, in some sense, to rational behaviour on the part of the players. All stable stationary points of the algorithm are shown to be Nash equilibria for the game. It is also shown that under some additional constraints on the game, the team will always converge to a Nash equilibrium.

A fully discrete C-0 interior penalty Galerkin approximation of the extended Fisher-Kolmogorov equation

A fully discrete C-0 interior penalty finite element method is proposed and analyzed for the Extended Fisher-Kolmogorov (EFK) equation u(t) + gamma Delta(2)u - Delta u + u(3) - u = 0 with appropriate initial and boundary conditions, where gamma is a positive constant. We derive a regularity estimate for the solution u of the EFK equation that is explicit in gamma and as a consequence we derive a priori error estimates that are robust in gamma. (C) 2013 Elsevier B.V. All rights reserved.

Discrete time second order sliding mode observer for uncertain linear multi-output system

This paper presents a second order sliding mode observer (SOSMO) design for discrete time uncertain linear multi-output system. The design procedure is effective for both matched and unmatched bounded uncertainties and/or disturbances. A second order sliding function and corresponding sliding manifold for discrete time system are defined similar to the lines of continuous time counterpart. A boundary layer concept is employed to avoid switching across the defined sliding manifold and the sliding trajectory is confined to a boundary layer once it converges to it. The condition for existence of convergent quasi-sliding mode (QSM) is derived. The observer estimation errors satisfying given stability conditions converge to an ultimate finite bound (within the specified boundary layer) with thickness O(T-2) where T is the sampling period. A relation between sliding mode gain and boundary layer is established for the existence of second order discrete sliding motion. The design strategy is very simple to apply and is demonstrated for three examples with different class of disturbances (matched and unmatched) to show the effectiveness of the design. Simulation results to show the robustness with respect to the measurement noise are given for SOSMO and the performance is compared with pseudo-linear Kalman filter (PLKF). (C) 2013 Published by Elsevier Ltd. on behalf of The Franklin Institute

Alternative Formulation of the Discrete Linear Quadratic Regulator (DLQR)

In this paper, an alternative apriori and aposteriori formulation has been derived for the discrete linear quadratic regulator (DLQR) in a manner analogous to that used in the discrete Kalman filter. It has been shown that the formulation seamlessly fits into the available formulation of the DLQR and the equivalent terms in the existing formulation and the proposed formulation have been identified. Thereafter, the significance of this alternative formulation has been interpreted in terms of the sensitivity of the controller performances to any changes in the states or to changes in the control inputs. The implications of this alternative formulation to adaptive controller tuning have also been discussed.

A Bacterial Foraging Optimization and Learning Automata Based Feature Selection for Motor Imagery EEG Classification

Selection of relevant features is an open problem in Brain-computer interfacing (BCI) research. Sometimes, features extracted from brain signals are high dimensional which in turn affects the accuracy of the classifier. Selection of the most relevant features improves the performance of the classifier and reduces the computational cost of the system. In this study, we have used a combination of Bacterial Foraging Optimization and Learning Automata to determine the best subset of features from a given motor imagery electroencephalography (EEG) based BCI dataset. Here, we have employed Discrete Wavelet Transform to obtain a high dimensional feature set and classified it by Distance Likelihood Ratio Test. Our proposed feature selector produced an accuracy of 80.291% in 216 seconds.

Using the system dynamics paradigm in teaching and learning technological university subjets

2nd International Conference on Education and New Learning Technologies

Optimal Data Distributions in Machine Learning

In the first part of the thesis we explore three fundamental questions that arise naturally when we conceive a machine learning scenario where the training and test distributions can differ. Contrary to conventional wisdom, we show that in fact mismatched training and test distribution can yield better out-of-sample performance. This optimal performance can be obtained by training with the dual distribution. This optimal training distribution depends on the test distribution set by the problem, but not on the target function that we want to learn. We show how to obtain this distribution in both discrete and continuous input spaces, as well as how to approximate it in a practical scenario. Benefits of using this distribution are exemplified in both synthetic and real data sets.

In order to apply the dual distribution in the supervised learning scenario where the training data set is fixed, it is necessary to use weights to make the sample appear as if it came from the dual distribution. We explore the negative effect that weighting a sample can have. The theoretical decomposition of the use of weights regarding its effect on the out-of-sample error is easy to understand but not actionable in practice, as the quantities involved cannot be computed. Hence, we propose the Targeted Weighting algorithm that determines if, for a given set of weights, the out-of-sample performance will improve or not in a practical setting. This is necessary as the setting assumes there are no labeled points distributed according to the test distribution, only unlabeled samples.

Finally, we propose a new class of matching algorithms that can be used to match the training set to a desired distribution, such as the dual distribution (or the test distribution). These algorithms can be applied to very large datasets, and we show how they lead to improved performance in a large real dataset such as the Netflix dataset. Their computational complexity is the main reason for their advantage over previous algorithms proposed in the covariate shift literature.

In the second part of the thesis we apply Machine Learning to the problem of behavior recognition. We develop a specific behavior classifier to study fly aggression, and we develop a system that allows analyzing behavior in videos of animals, with minimal supervision. The system, which we call CUBA (Caltech Unsupervised Behavior Analysis), allows detecting movemes, actions, and stories from time series describing the position of animals in videos. The method summarizes the data, as well as it provides biologists with a mathematical tool to test new hypotheses. Other benefits of CUBA include finding classifiers for specific behaviors without the need for annotation, as well as providing means to discriminate groups of animals, for example, according to their genetic line.

Learning the Structure of Deep Sparse Graphical Models

Deep belief networks are a powerful way to model complex probability distributions. However, learning the structure of a belief network, particularly one with hidden units, is difficult. The Indian buffet process has been used as a nonparametric Bayesian prior on the directed structure of a belief network with a single infinitely wide hidden layer. In this paper, we introduce the cascading Indian buffet process (CIBP), which provides a nonparametric prior on the structure of a layered, directed belief network that is unbounded in both depth and width, yet allows tractable inference. We use the CIBP prior with the nonlinear Gaussian belief network so each unit can additionally vary its behavior between discrete and continuous representations. We provide Markov chain Monte Carlo algorithms for inference in these belief networks and explore the structures learned on several image data sets.

Information theory, inference, and learning algorithms

Fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.

Reinforcement learning using a continuous time actor-critic framework with spiking neurons.

Animals repeat rewarded behaviors, but the physiological basis of reward-based learning has only been partially elucidated. On one hand, experimental evidence shows that the neuromodulator dopamine carries information about rewards and affects synaptic plasticity. On the other hand, the theory of reinforcement learning provides a framework for reward-based learning. Recent models of reward-modulated spike-timing-dependent plasticity have made first steps towards bridging the gap between the two approaches, but faced two problems. First, reinforcement learning is typically formulated in a discrete framework, ill-adapted to the description of natural situations. Second, biologically plausible models of reward-modulated spike-timing-dependent plasticity require precise calculation of the reward prediction error, yet it remains to be shown how this can be computed by neurons. Here we propose a solution to these problems by extending the continuous temporal difference (TD) learning of Doya (2000) to the case of spiking neurons in an actor-critic network operating in continuous time, and with continuous state and action representations. In our model, the critic learns to predict expected future rewards in real time. Its activity, together with actual rewards, conditions the delivery of a neuromodulatory TD signal to itself and to the actor, which is responsible for action choice. In simulations, we show that such an architecture can solve a Morris water-maze-like navigation task, in a number of trials consistent with reported animal performance. We also use our model to solve the acrobot and the cartpole problems, two complex motor control tasks. Our model provides a plausible way of computing reward prediction error in the brain. Moreover, the analytically derived learning rule is consistent with experimental evidence for dopamine-modulated spike-timing-dependent plasticity.

Learning Fine Motion by Markov Mixtures of Experts

Compliant control is a standard method for performing fine manipulation tasks, like grasping and assembly, but it requires estimation of the state of contact between the robot arm and the objects involved. Here we present a method to learn a model of the movement from measured data. The method requires little or no prior knowledge and the resulting model explicitly estimates the state of contact. The current state of contact is viewed as the hidden state variable of a discrete HMM. The control dependent transition probabilities between states are modeled as parametrized functions of the measurement We show that their parameters can be estimated from measurements concurrently with the estimation of the parameters of the movement in each state of contact. The learning algorithm is a variant of the EM procedure. The E step is computed exactly; solving the M step exactly would require solving a set of coupled nonlinear algebraic equations in the parameters. Instead, gradient ascent is used to produce an increase in likelihood.

Learning Unions of Rectangles with Queries

We investigate the efficient learnability of unions of k rectangles in the discrete plane (1,...,n)[2] with equivalence and membership queries. We exhibit a learning algorithm that learns any union of k rectangles with O(k^3log n) queries, while the time complexity of this algorithm is bounded by O(k^5log n). We design our learning algorithm by finding "corners" and "edges" for rectangles contained in the target concept and then constructing the target concept from those "corners" and "edges". Our result provides a first approach to on-line learning of nontrivial subclasses of unions of intersections of halfspaces with equivalence and membership queries.

Learning and Production of Movement Sequences: Behavioral, Neurophysiological, and Modeling Perspectives

A growing wave of behavioral studies, using a wide variety of paradigms that were introduced or greatly refined in recent years, has generated a new wealth of parametric observations about serial order behavior. What was a mere trickle of neurophysiological studies has grown to a more steady stream of probes of neural sites and mechanisms underlying sequential behavior. Moreover, simulation models of serial behavior generation have begun to open a channel to link cellular dynamics with cognitive and behavioral dynamics. Here we summarize the major results from prominent sequence learning and performance tasks, namely immediate serial recall, typing, 2XN, discrete sequence production, and serial reaction time. These populate a continuum from higher to lower degrees of internal control of sequential organization. The main movement classes covered are speech and keypressing, both involving small amplitude movements that are very amenable to parametric study. A brief synopsis of classes of serial order models, vis-à-vis the detailing of major effects found in the behavioral data, leads to a focus on competitive queuing (CQ) models. Recently, the many behavioral predictive successes of CQ models have been joined by successful prediction of distinctively patterend electrophysiological recordings in prefrontal cortex, wherein parallel activation dynamics of multiple neural ensembles strikingly matches the parallel dynamics predicted by CQ theory. An extended CQ simulation model-the N-STREAMS neural network model-is then examined to highlight issues in ongoing attemptes to accomodate a broader range of behavioral and neurophysiological data within a CQ-consistent theory. Important contemporary issues such as the nature of working memory representations for sequential behavior, and the development and role of chunks in hierarchial control are prominent throughout.

Team-teaching for inclusive learning: Purposes, practices and perceptions of a team-teaching initiative in Irish post-primary schools

Background. Schools unequivocally privilege solo-teaching. This research seeks to enhance our understanding of team-teaching by examining how two teachers, working in the same classroom at the same time, might or might not contribute to the promotion of inclusive learning. There are well-established policy statements that encourage change and moves towards the use of team-teaching to promote greater inclusion of students with special educational needs in mainstream schools and mainstream classrooms. What is not so well established is the practice of team-teaching in post-primary settings, with little research conducted to date on how it can be initiated and sustained, and a dearth of knowledge on how it impacts upon the students and teachers involved. Research questions and aims. In light of the paucity and inconclusive nature of the research on team-teaching to date (Hattie, 2009), the orientating question in this study asks ‘To what extent, can the introduction of a formal team-teaching initiative enhance the quality of inclusive student learning and teachers’ learning at post-primary level?’ The framing of this question emerges from ongoing political, legal and educational efforts to promote inclusive education. The study has three main aims. The first aim of this study is to gather and represent the voices and experiences of those most closely involved in the introduction of team-teaching; students, teachers, principals and administrators. The second aim is to generate a theory-informed understanding of such collaborative practices and how they may best be implemented in the future. The third aim is to advance our understandings regarding the day-to-day, and moment-to-moment interactions, between teachers and students which enable or inhibit inclusive learning. Sample. In total, 20 team-teaching dyads were formed across seven project schools. The study participants were from two of the seven project schools, Ash and Oak. It involved eight teachers and 53 students, whose age ranged from 12-16 years old, with 4 teachers forming two dyads per school. In Oak there was a class of first years (n=11) with one dyad and a class of transition year students (n=24) with the other dyad. In Ash one class group (n=18) had two dyads. The subjects in which the dyads engaged were English and Mathematics. Method. This research adopted an interpretive paradigm. The duration of the fieldwork was from April 2007 to June 2008. Research methodologies included semi-structured interviews (n=44), classroom observation (n=20), attendance at monthly teacher meetings (n=6), questionnaires and other data gathering practices which included school documentation, assessment findings and joint examination of student work samples (n=4). Results. Team-teaching involves changing normative practices, and involves placing both demands and opportunities before those who occupy classrooms (teachers and students) and before those who determine who should occupy these classrooms (principals and district administrators). This research shows how team-teaching has the potential to promote inclusive learning, and when implemented appropriately, can impact positively upon the learning experiences of both teachers and students. The results are outlined in two chapters. In chapter four, Social Capital Theory is used in framing the data, the change process of bonding, bridging and linking, and in capturing what the collaborative action of team-teaching means, asks and offers teachers; within classes, between classes, between schools and within the wider educational community. In chapter five, Positioning Theory deductively assists in revealing the moment-to-moment, dynamic and inclusive learning opportunities, that are made available to students through team-teaching. In this chapter a number of vignettes are chosen to illustrate such learning opportunities. These two theories help to reveal the counter-narrative that team-teaching offers, regarding how both teachers and students teach and learn. This counter-narrative can extend beyond the field of special education and include alternatives to the manner in which professional development is understood, implemented, and sustained in schools and classrooms. Team-teaching repositions teachers and students to engage with one another in an atmosphere that capitalises upon and builds relational trust and shared cognition. However, as this research study has found, it is wise that the purposes, processes and perceptions of team-teaching are clear to all so that team-teaching can be undertaken by those who are increasingly consciously competent and not merely accidentally adequate. Conclusions. The findings are discussed in the context of the promotion of effective inclusive practices in mainstream settings. I believe that such promotion requires more nuanced understandings of what is being asked of, and offered to, teachers and students. Team-teaching has, and I argue will increasingly have, its place in the repertoire of responses that support effective inclusive learning. To capture and extend such practice requires theoretical frameworks that facilitate iterative journeys between research, policy and practice. Research to date on team-teaching has been too focused on outcomes over short timeframes and not focused enough on the process that is team-teaching. As a consequence team-teaching has been under-used, under-valued, under-theorised and generally not very well understood. Moving from classroom to staff room and district board room, theoretical frameworks used in this research help to travel with, and understand, the initiation, engagement and early consequences of team-teaching within and across the educational landscape. Therefore, conclusions from this study have implications for the triad of research, practice and policy development where efforts to change normative practices can be matched by understandings associated with what it means to try something new/anew, and what it means to say it made a positive difference.